lmompe3 {lmomco} | R Documentation

## L-moments of the Pearson Type III Distribution

### Description

This function estimates the L-moments of the Pearson Type III distribution given the parameters (μ, σ, and gamma) from `parpe3`. The L-moments in terms of the parameters are complicated and solved numerically.

For the implementation in the lmomco package, the three parameters are μ, σ, and gamma for the mean, standard deviation, and skew, respectively. Therefore, the Pearson Type III distribution is of considerable theoretical interest to this package because the parameters, which are estimated via the L-moments, are in fact the product moments. Although, these values fitted by the method of L-moments will not be numerically equal to the sample product moments. Further details are provided in the examples section of the `pmoms` function documentation.

### Usage

    lmompe3(para)

### Arguments

`para` | The parameters of the distribution.

### Value

An R `list` is returned.

`L1` | Arithmetic mean.
`L2` | L-scale—analogous to standard deviation.
`LCV` | coefficient of L-variation—analogous to coe. of variation.
`TAU3` | The third L-moment ratio or L-skew—analogous to skew.
`TAU4` | The fourth L-moment ratio or L-kurtosis—analogous to kurtosis.
`TAU5` | The fifth L-moment ratio.
`L3` | The third L-moment.
`L4` | The fourth L-moment.
`L5` | The fifth L-moment.
`source` | An attribute identifying the computational source of the L-moments: “lmompe3”.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`parpe3`, `quape3`, `cdfpe3`

### Examples

    lmr <- lmom.ub(c(123,34,4,654,37,78))
    lmr
    lmompe3(parpe3(lmr))

[Package lmomco version 0.92 Index]